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+//Chapter 6
+//Example 6.3
+//page 201
+//To find an approximate load flow solution
+clear;clc;
+
+/////////////////////////////////////////////////////////////////////////////////
+//Realdemand    Reactive demand    Real generation    Reactive generation     Bus
+/////////////////////////////////////////////////////////////////////////////////
+  Pd1=1;           Qd1=0.5;            Pg1=0;          Qg1=0;//initialization  1
+  Pd2=1;           Qd2=0.4;            Pg2=4;          Qg2=0;//initialization  2
+  Pd3=2;           Qd3=1;              Pg3=0;          Qg3=0;//initialization  3
+  Pd4=2;           Qd4=1;              Pg4=0;          Qg4=0;//initialization  4
+
+Pg1=Pd1+Pd2+Pd3+Pd4-Pg2;
+
+//Ybus matrix from the network
+Ybus=[-21.667*%i 5*%i 6.667*%i 10*%i;
+      5*%i -21.667*%i 10*%i 6.667*%i;
+      6.667*%i 10*%i -16.667*%i 0;
+      10*%i 6.667*%i 0 -16.667*%i];
+printf('Ybus matrix of the system is given by \nYbus=');disp(Ybus);
+//as given in the text book using approximate load flow equations and simplifying (ii),(iii),(iv)
+//delta matrix(x) is of the from A*x=B
+A=[-5 21.667 -10 -6.667;
+   -6.667 -10 16.667 0;
+   -10 -6.667 0 16.667
+   1 0 0 0];
+   
+B=[3; -2; -2;0];
+
+delta=inv(A)*B; //solving for delta
+printf('\nDelta of the system is given by \ndelta(rad)=');disp(delta);
+
+Q1=-5*cos(delta(2,1))-6.667*cos(delta(3,1))-10*cos(delta(4,1))+21.667;
+Q2=-5*cos(delta(2,1))-10*cos(delta(3,1)-delta(2,1))-6.667*cos(delta(4,1)-delta(2,1))+21.667;
+Q3=-6.667*cos(delta(3,1))-10*cos(delta(3,1)-delta(2,1))+16.667;
+Q4=-10*cos(delta(4,1))-6.667*cos(delta(4,1)-delta(2,1))+16.667;
+
+Q=[Q1;Q2;Q3;Q4];
+printf('\nInjected reactive power at the buses is given by \nQi(in pu)=');disp(Q);
+
+Qg1=Q1+Qd1;
+Qg2=Q2+Qd2;
+Qg3=Q3+Qd3;
+Qg4=Q4+Qd4;
+
+Qg=[Qg1;Qg2;Qg3;Qg4];
+printf('\n Reactive power generation at the four buses are \nQgi(in pu)=');disp(Qg);
+Qd=[Qd1;Qd2;Qd3;Qd4];
+Ql=sum(Qg)-sum(Qd);
+printf('\nReactive power losses are QL=%0.5f pu',Ql);
+
+printf('\n\nLine Flows are given as:\n');
+P13=(abs(Ybus(1,3)))*sin(delta(1,1)-delta(3,1));P31=-P13;printf('\nP13=-P31=%0.3f pu',P13);
+P12=(abs(Ybus(1,2)))*sin(delta(1,1)-delta(2,1));P21=-P12;printf('\nP12=-P21=%0.3f pu',P12);
+P14=(abs(Ybus(1,4)))*sin(delta(1,1)-delta(4,1));P41=-P14;printf('\nP14=-P41=%0.3f pu',P14);
+
+Q13=abs(Ybus(1,3))-(abs(Ybus(1,3)))*cos(delta(1,1)-delta(3,1));Q31=-Q13;printf('\n\nQ13=-Q31=%0.3f pu',Q13);
+Q12=abs(Ybus(1,2))-(abs(Ybus(1,2)))*cos(delta(1,1)-delta(2,1));Q21=-Q12;printf('\nQ12=-Q21=%0.3f pu',Q12);
+Q14=abs(Ybus(1,4))-(abs(Ybus(1,4)))*cos(delta(1,1)-delta(4,1));Q41=-Q14;printf('\nQ14=-Q41=%0.3f pu',Q14);
+
+
+   
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